A new analytical method for designing centralised PI controllers for unstable systems using a direct synthesis approach

This paper introduces a new analytical technique using a direct synthesis strategy to develop centralised proportional–integral (PI) controllers for multivariable processes. The current method design controller is focused on attaining the desired closed-loop response for multi input multi output (MIMO) processes that involve multiple time delays. The conventional multivariable PI controller is obtained by approximating the ideal multivariable controller by the Maclaurin series expansion. This is accomplished by choosing the desired closed-loop response order as the system order plus two. Subsequent analysis investigates the proposed method’s efficacy in designing multivariable PI controllers. Servo and regulatory problems studies were conducted to find the effectiveness of the proposed method and compared it with other methods recently reported in the literature, as well as assessment of performance indices like integral absolute error (IAE) and integral square error (ISE). The proposed controller's robustness is assessed by plotting the inverse maximum singular value against frequency, both input and output multiplicative uncertainties.